 Electromagnetism involves vector fields. Let's take a look at how we can visualize these. When communicating ideas with others, you want to be as clear as possible. Using diagrams generally helps with this. However, it doesn't help if you have confusing diagrams. This is especially important for fields. Because we don't see fields in our daily lives, it's hard for us to visualize it. You want the diagrams representing fields to be extra clear. This is the vector field representation of a gravitational field around a moon. The magnitude of the vector represents the strength of the field. So every vector represents the direction and strength of the gravitational field at a point. There are a lot of vectors in this picture. And sometimes, where there is a strong field, the vectors overlap each other. This is confusing to look at and make sense of, so let's use a different representation for clarity. This is the field line representation of a gravitational field around a moon, where instead of drawing vectors at every point, we use lines. These lines come from joining together the vectors in such a way that the vectors are tangent to the line at every point. The direction of lines tells us the direction of the gravitational field, and the density of lines tells us the strength of the field. The more dense the lines are, the stronger the field, and vice versa. So these field lines tell us that gravity is stronger, closer to the moon, and weaker further out, which matches with expectation. Field lines can be used to represent some types of vector fields, gravitational fields, electric fields, and magnetic fields, just to name a few. One example of a vector field that can be represented using field lines is a magnetic field. Magnetic fields are invisible. One could even question the existence of them. However, the classic iron filings experiment shows that magnetic fields are indeed real and not imaginary. We want to see the magnetic field around this magnet. If I place a book and a piece of paper on top of it, we can see the iron filings clearer. Sprinkling on the iron filings so that they fall naturally in place, we can see lines forming. Each of these iron filings act like little vectors, but since they are so small, when they join head to tail, they basically form a line. So this is the magnetic field around a magnet. If we look at these sideways, we can see some iron filings sticking straight up. This tells us that the magnetic field surrounding a bar magnet is three-dimensional. Here is another tool for visualizing magnetic fields. This contains iron filings floating around in liquid inside it. At the center, there is a bar magnet. If I shake this so that the iron filings are dispersed evenly, and then place the bar magnet inside it, we can see field lines starting to fall. Now, rotating this, we can see field lines are three-dimensional and forming all around the magnet.